IMHO, a small 1x30 (or 1x42) belt sander is perfect for sharpening. You can get a 1x30 at
www.harborfreight.com right now for $30 w/free shipping. Go to Lowe's for the 1x42 for $99 (also has a disk sander).
Start out with 220 grit belts to set the edge. At the speed they run, you don't want any lower grit unless you're doing major reprofiling.
Then go to 400 grit (equal passes & same angle on both sides).
Go slowly at first...even at these grits, you can really peel the metal off quickly.
Then either a felt belt or a leather belt (both can be purchased at
www.leevalleytools.com) for polishing/stropping.
For the 220 and 400 grit belts, get Aluminum Oxide "X" weight belts from
Discount Abrasives
IIRC, you can mix-and-match the "X" weight belts. That is, get a few 220, a few 400 and maybe a 180 and a 600 just for fun.
Understand that this is a good "starter set" and you'll likely find belts you like and don't like the more you sharpen. That said, the 1x30 and $10 worth of belts is a quick, easy, and inexpensive way to get into sharpening.